Question

5. B) Now consider that RandomCorp decides to issue another bond with similar characteristics as above; but with two major changes. First, it decides to pay the coupon semi-annually. Second, given the seasonality of its cashflows, it pays differential coupons as - paying $60 in the first half of a calendar year and $40 in the second half. Calculate the duration of this bond. [7 pts]

Answer 1

5A
Years	Cashflow	Present value formula	Present value	Duration D = (PV*T)
1	100	100/(1+8%)^1	92.59259259	92.59
2	1100	1100/(1+8%)^2	943.0727023	1886.15
Total	1035.67	1978.74
Macaulay Duration = Duration D / Present value of cashflows	Macaulay Duration = 1978.74 / 1035.67 = 1.91
5B
Years	Cashflow	Present value formula	Present value	Duration D = (PV*T)
0.5	60	60/(1+4%)^0.5	58.83484054	29.42
1	40	40/(1+4%)^1	38.46153846	38.46
1.5	60	60/(1+4%)^1.5	56.57196206	84.86
2	1040	1040/(1+4%)^2	961.5384615	1923.08
Total	1115.41	2075.81
Macaulay Duration = Duration D / Present value of cashflows	Macaulay Duration = 2075.81 / 1115.41 = 1.86